Google for "night blooming cereus" and see if you find a photo like your cactus. Do the same with "orchid cactus" and eventually maybe you can identify it for yourself. Without a photo anything you're told will be a guess.

A good resource book you may find at the library is Peter Loewer's 'The Evening Garden.' There's a whole chapter of night blooming cereuses. I found mine; perhaps you'll find yours.

Nell

The plant with flat leaves is an Orchid Cactus or Dutchman's Pipe, the Night Blooming Cirrus is an ordinary looking climbing cactus, see http://aboatbuildingjournal.com/night_blooming_cirrus_in_paradise.htm the confusion occurs because the blooms are almost identical.

Your plant is probably an epiphyllum cactus. Which cereus is a synonym of.